An Essay towards Solving a Problem in the Doctrine of Chances¶
Bayes, T. (1763). An Essay towards Solving a Problem in the Doctrine of Chances. Philosophical Transactions of the Royal Society of London, 53, 370-418.
Cited by¶
9 citations across 9 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Bayesian Updating
- (1) **Bayesian updating is the systematic process of revising a probability distribution over possibilities — the prior — by combining it with the likelihood of new evidence given each possibility, producing a revised posterior distribution.** (2) Mathematically, posterior ∝ prior × likelihood (Bayes' theorem
This source(Communicated posthumously by Richard Price.) Founding statement of inverse-probability reasoning / Bayes' theorem. SUPPORTS marker 007 (posterior ∝ prior × likelihood).
- (1) **Bayesian updating is the systematic process of revising a probability distribution over possibilities — the prior — by combining it with the likelihood of new evidence given each possibility, producing a revised posterior distribution.** (2) Mathematically, posterior ∝ prior × likelihood (Bayes' theorem
- Conditional Probability
- Two further facts come along for the ride: conditional independence (\(P(A \mid B,C) = P(A \mid C)\)), the structural primitive that makes graphical models and large-scale inference tractable by declaring some conditioning irrelevant given other conditioning; and Bayes' rule (\(P(A \mid B) = P(B \mid A)\,P(A)/P(B)\)), the algebraic relation that inverts the direction of conditioning
This sourceThe original statement of the rule inverting the direction of conditioning, P(A|B) = P(B|A)P(A)/P(B).
- Two further facts come along for the ride: conditional independence (\(P(A \mid B,C) = P(A \mid C)\)), the structural primitive that makes graphical models and large-scale inference tractable by declaring some conditioning irrelevant given other conditioning; and Bayes' rule (\(P(A \mid B) = P(B \mid A)\,P(A)/P(B)\)), the algebraic relation that inverts the direction of conditioning
- Evidence
- The inference rule is Bayes' theorem: the posterior \(P(D\mid +) = \frac{P(+\mid D)\,P(D)}{P(+)}\), which makes the prime's defeasibility/weight-bearing invariant exact — a positive test does not deduce disease, it shifts a prior to a graded posterior.
This sourceOriginal statement of the inverse-probability rule underlying Bayesian updating of a hypothesis on observed evidence.
- The inference rule is Bayes' theorem: the posterior \(P(D\mid +) = \frac{P(+\mid D)\,P(D)}{P(+)}\), which makes the prime's defeasibility/weight-bearing invariant exact — a positive test does not deduce disease, it shifts a prior to a graded posterior.
- False Positive Paradox
- The false positive paradox is the structural fact that when a binary detector is applied to a population in which the target condition is rare, most of the positives it flags will be wrong — even when the detector has high sensitivity and high specificity.
This sourceOriginal statement of Bayes' rule, by which posterior odds equal prior odds times the likelihood ratio — the arithmetic underlying the base-rate dependence of positive predictive value.
- The false positive paradox is the structural fact that when a binary detector is applied to a population in which the target condition is rare, most of the positives it flags will be wrong — even when the detector has high sensitivity and high specificity.
- Inversion
- The Bayesian inversion pattern
This source(Posthumous publication communicated by Richard Price.) Founding text of inverse-probability reasoning that becomes the Bayesian interpretation, mechanizing the update of prior probabilities by conditioning on observed evidence.
- The Bayesian inversion pattern
- Probability
- Computer science and machine learning use probability for randomized algorithms, probabilistic graphical models, Bayesian inference, Monte Carlo methods, information theory (Shannon entropy as the expected log-probability of a code), and reinforcement learning under uncertain dynamics. Decision-making and economics rest on expected utility theory, risk pricing, insurance, portfolio theory, and game theory with mixed strategies — most of the structure traceable to Bayes' (1763) originating insight on inverse probability.
This source(Posthumous publication communicated by Richard Price.) Founding text of inverse-probability reasoning that becomes the Bayesian interpretation, mechanizing the update of prior probabilities by conditioning on observed evidence.
Supported in partVerified against the publisher's abstract
Confirms the item is Bayes' posthumous essay of 1763 communicated by Price, matching the citation's parenthetical, but holds no text of the essay, so the conditioning rule it is cited for is not shown here.
“I Now send you an essay which I have found among the papers of our deceased friend Mr. Bayes, and which, in my opinion, has great merit, and well deserves to be preserved.”
- Computer science and machine learning use probability for randomized algorithms, probabilistic graphical models, Bayesian inference, Monte Carlo methods, information theory (Shannon entropy as the expected log-probability of a code), and reinforcement learning under uncertain dynamics. Decision-making and economics rest on expected utility theory, risk pricing, insurance, portfolio theory, and game theory with mixed strategies — most of the structure traceable to Bayes' (1763) originating insight on inverse probability.
Domain-specific¶
Mechanisms¶
- Confidence Update Worksheet
- Done honestly it is disciplined Bayesian bookkeeping,
This sourceProvides the inverse-probability rule underlying Bayesian updating from prior information and observed evidence.
- Done honestly it is disciplined Bayesian bookkeeping,
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 1 of 9 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:f91d6ed1dabf · see in the full table